PatchSizePilot

PatchSizePilot

Overview

Meta-ecosystems have been studied looking at meta-ecosystems in which patch size was the same. However, of course, we know that meta-ecosystems are mad out of patches that have different size. To see the effects of patch size on meta-ecosystem properties, we ran a four weeks protist experiment in which different ecosystems were connected through the flow of nutrients. The flow of nutrients resulted from a perturbation of the ecosystems in which a fixed part of the cultures was boiled and then poored into the receiving patch. This had a fixed volume (e.g., small perturbation = 6.75 ml) and was the same across all patch sizes. The experiment design consisted in crossing two disturbances with a small, medium, and large isolated ecosystems and with a small-small, medium-medium, large-large, and small-large meta-ecosystem. We took videos every four days and we create this perturbation and resource flow the day after taking videos. We skipped the perturbation the day after we assembled the experiment so that we would start perturbing it when population densities were already high.

We had mainly two research questions:

• Do local properties of a patch depend upon the size of the patch it is connected to?

• Do regional properties of a meta-ecosystem depend upon the relative size of its patch?

Biomass

Aim

Here I study how biomass density changes across treatments in the PatchSizePilot. In particular, my research questions are:

• How does biomass density change regionally?

  • Do meta-ecosystems with the same total size but with patches that are either the same size or of different size have a different biomass density? (Do the medium-medium and small-large meta-ecosystems have different biomass density?)

  • And if they do, is it because of resource flow? Or would we see this also with small and large ecosystems that are not connected? (Do the small-large meta-ecosystems have different biomass density from two isolated small and large patches?)

• How does biomass density change locally?
  • How does biomass density change according to the size to which the patch is connected? (Does a small patch connected to a small patch have the same biomass density than a small patch connected to a large patch? And does a large patch connected to a large patch have the same biomass density than a large patch connected to a small patch?)

Data

Experimental cultures

culture_info = read.csv(here("data", "PatchSizePilot_culture_info.csv"), header = TRUE)

datatable(culture_info[,1:10],
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Local biomass dataset

### --- IMPORT --- ###

load(here("data", "population", "t0.RData")); t0 = pop_output
load(here("data", "population", "t1.RData")); t1 = pop_output
load(here("data", "population", "t2.RData")); t2 = pop_output
load(here("data", "population", "t3.RData")); t3 = pop_output
load(here("data", "population", "t4.RData")); t4 = pop_output
load(here("data", "population", "t5.RData")); t5 = pop_output
load(here("data", "population", "t6.RData")); t6 = pop_output
load(here("data", "population", "t7.RData")); t7 = pop_output
rm(pop_output)

### --- TIDY --- ###

#Column: time
t0$time = NA
t1$time = NA

#Column: replicate_video
t0$replicate_video = 1:12 #In t1 I took 12 videos of a single 
t1$replicate_video = 1 #In t1 I took only 1 video/culture
t2$replicate_video = 1 #In t2 I took only 1 video/culture
t3$replicate_video = 1 #In t3 I took only 1 video/culture
t4$replicate_video = 1 #In t4 I took only 1 video/culture
t5$replicate_video = 1 #In t5 I took only 1 video/culture
t6 = t6 %>%
  rename(replicate_video = replicate)
t7 = t7 %>%
  rename(replicate_video = replicate)

#Create an elongated version of t0 so that each of the 110 cultures can have 12 video replicates at t0.
elongating_t0 = NULL
for (video in 1:nrow(t0)){
  
  for (ID in 1:nrow(culture_info)) {
    
    elongating_t0 = rbind(elongating_t0, t0[video,])
    
    }

  }

ID_vector = rep(1:nrow(culture_info), 
                times = nrow(t0))

elongating_t0$culture_ID = ID_vector

#Merge previous data-sets
t0 = merge(culture_info,elongating_t0, by="culture_ID")
t1 = merge(culture_info,t1, by = "culture_ID")
t2 = merge(culture_info,t2, by = "culture_ID")
t3 = merge(culture_info,t3, by = "culture_ID")
t4 = merge(culture_info,t4, by = "culture_ID")
t5 = merge(culture_info,t5, by = "culture_ID")
t6 = merge(culture_info,t6, by = "culture_ID")
t7 = merge(culture_info,t7, by = "culture_ID")
ds_biomass = rbind(t0, t1, t2, t3, t4, t5, t6, t7)
rm(elongating_t0, t0, t1, t2, t3, t4, t5, t6, t7)

#Column: time_point
ds_biomass$time_point[ds_biomass$time_point=="t0"] = 0
ds_biomass$time_point[ds_biomass$time_point=="t1"] = 1
ds_biomass$time_point[ds_biomass$time_point=="t2"] = 2
ds_biomass$time_point[ds_biomass$time_point=="t3"] = 3
ds_biomass$time_point[ds_biomass$time_point=="t4"] = 4
ds_biomass$time_point[ds_biomass$time_point=="t5"] = 5
ds_biomass$time_point[ds_biomass$time_point=="t6"] = 6
ds_biomass$time_point[ds_biomass$time_point=="t7"] = 7
ds_biomass$time_point = as.character(ds_biomass$time_point)

#Column: day
ds_biomass$day = NA
ds_biomass$day[ds_biomass$time_point== 0] = 0
ds_biomass$day[ds_biomass$time_point== 1] = 4
ds_biomass$day[ds_biomass$time_point== 2] = 8
ds_biomass$day[ds_biomass$time_point== 3] = 12
ds_biomass$day[ds_biomass$time_point== 4] = 16
ds_biomass$day[ds_biomass$time_point== 5] = 20
ds_biomass$day[ds_biomass$time_point== 6] = 24
ds_biomass$day[ds_biomass$time_point== 7] = 28

#Column: size_of_connected_patch
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "S"] = "S"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "S (S_S)"] = "S"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "S (S_L)"] = "L"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "M (M_M)"] = "M"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "L"] = "L"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "L (L_L)"] = "L"
ds_biomass$size_of_connected_patch[ds_biomass$eco_metaeco_type == "L (S_L)"] = "S"

#Column: eco_metaeco_type
ds_biomass$eco_metaeco_type = factor(ds_biomass$eco_metaeco_type, 
                             levels = c('S', 
                                        'S (S_S)', 
                                        'S (S_L)', 
                                        'M', 
                                        'M (M_M)', 
                                        'L', 
                                        'L (L_L)', 
                                        'L (S_L)'))

ds_biomass = ds_biomass %>%
  filter(! culture_ID %in% ecosystems_to_take_off)

ds_for_evaporation = ds_biomass

ds_biomass = ds_biomass %>% 
  select(culture_ID, 
         patch_size,
         patch_size_volume,
         disturbance, 
         metaecosystem_type, 
         bioarea_per_volume, 
         replicate_video, 
         time_point,
         day,
         metaecosystem, 
         system_nr, 
         eco_metaeco_type,
         size_of_connected_patch) %>%
  relocate(culture_ID,
           system_nr,
           disturbance,
           time_point,
           day,
           patch_size,
           patch_size_volume,
           metaecosystem,
           metaecosystem_type,
           eco_metaeco_type,
           size_of_connected_patch,
           replicate_video,
           bioarea_per_volume)

datatable(ds_biomass,
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Regional biomass data set

ds_regional_biomass = ds_biomass %>%
  filter(metaecosystem == "yes") %>%
  filter(! system_nr %in% metaecosystems_to_take_off) %>%
  group_by(culture_ID, 
           system_nr, 
           disturbance, 
           time_point,
           day, 
           patch_size,
           patch_size_volume,
           metaecosystem_type) %>%
  summarise(bioarea_per_volume_video_averaged = mean(bioarea_per_volume)) %>%
  mutate(total_patch_bioarea = bioarea_per_volume_video_averaged * patch_size_volume) %>%
  group_by(system_nr, 
           disturbance, 
           time_point,
           day,
           metaecosystem_type) %>%
  summarise(total_regional_bioarea = sum(total_patch_bioarea))

### --- TABLE --- ###

datatable(ds_regional_biomass,
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Local biomass lnRR data-set

for (disturbance_input in c("low", "high")){
  for (eco_metaeco_input in c("S", "M", "L")){
    for (time_point_input in 0:7){
      
      ds_biomass$isolated_control[ds_biomass$patch_size == eco_metaeco_input & 
                              ds_biomass$disturbance == disturbance_input &
                              ds_biomass$time_point == time_point_input] = 
        
        ds_biomass %>%
        filter(disturbance == disturbance_input) %>%
        filter(eco_metaeco_type == eco_metaeco_input) %>%
        filter(time_point == time_point_input) %>%        
        group_by(culture_ID) %>%
        summarise(bioarea_per_volume_across_videos = mean(bioarea_per_volume)) %>%
        summarise(mean_bioarea_per_volume = mean(bioarea_per_volume_across_videos))
      
    }
  }
}

ds_biomass_averaged_across_videos =  ds_biomass %>%
  mutate(isolated_control = as.numeric(isolated_control)) %>%
  group_by(disturbance, 
           eco_metaeco_type, 
           culture_ID, 
           day,
           time_point,
           isolated_control) %>%
  summarise(bioarea_per_volume = mean(bioarea_per_volume))

ds_biomass_averaged_across_videos %>%
  mutate(RR_bioarea_per_volume = (bioarea_per_volume_across_videos+1) /isolated_control) %>%
  mutate(lnRR_bioarea_per_volume = ln(RR_bioarea_per_volume))

datatable(ds_biomass_averaged_across_videos,
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Regional biomass

Medium-Medium vs Small-Large

Do meta-ecosystems with the same total size but with patches that are either the same size or of different size have a different biomass density? (Do the medium-medium and small-large meta-ecosystems have different biomass density?)

Plots

ds_regional_biomass %>%
    filter ( disturbance == "low") %>%
    filter (metaecosystem_type == "S_L" | 
              metaecosystem_type == "M_M") %>%
    ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
                color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (µm²?)",
         title = "Disturbance = low",
         fill = "System nr",
         color = "System nr",
         linetype = "") +
    scale_x_continuous(limits = c(-2, 30)) +
    scale_linetype_discrete(labels = c("medium-medium",
                                     "small-large")) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

ds_regional_biomass %>%
    filter ( disturbance == "high") %>%
    filter (metaecosystem_type == "S_L" | metaecosystem_type == "M_M") %>%
    ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
                color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (µm²?)",
         title = "Disturbance = high",
         fill = "System nr",
         color = "System nr",
         linetype = "") +
    scale_x_continuous(limits = c(-2, 30)) +
    scale_linetype_discrete(labels = c("medium-medium",
                                     "small-large")) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

regional_publication = ds_regional_biomass %>%
  filter(disturbance == "low") %>%
  filter (metaecosystem_type == "S_L" | metaecosystem_type == "M_M") %>%
  ggplot (aes(x = day,
              y = total_regional_bioarea,
              group = interaction(day, metaecosystem_type),
              fill = metaecosystem_type)) +
  geom_boxplot() +
  labs(x = "Day", 
       y = "Regional bioarea (µm²?)",
       title = "Disturbance = low",
       color='', 
       fill='') +
  scale_fill_discrete(labels = c("medium-medium", 
                                 "small-large")) +
  theme_bw() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(),
        legend.position = c(.95, .95),
        legend.justification = c("right", "top"),
        legend.box.just = "right",
        legend.margin = margin(6, 6, 6, 6))  +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")
regional_publication

ds_regional_biomass %>%
  filter(disturbance == "high") %>%
  filter (metaecosystem_type == "S_L" | metaecosystem_type == "M_M") %>%
  ggplot (aes(x = day,
              y = total_regional_bioarea,
              group = interaction (day, metaecosystem_type),
              fill = metaecosystem_type)) +
  geom_boxplot() +
  labs(x = "Day", 
       y = "Regional bioarea (µm²?)",
       title = "Disturbance = high",
       color='', 
       fill='') +
  scale_fill_discrete(labels = c("medium-medium", 
                                 "small-large")) +
  theme_bw() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(),
        legend.position = c(.95, .95),
        legend.justification = c("right", "top"),
        legend.box.just = "right",
        legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

Model time series

How does the biomass density of medium-medium and small-large meta-ecosystems differ across the time series? (The first two points before the first disturbance are taken off).

Let’s see how linear is the time trend of bioarea and if we can make it more linear with a log10 transformation. We are lucky that during the modelling process we need to drop the first two time points because they were before the first perturbation.

Linearity of regional bioarea ~ time

ds_regional_biomass %>%
  filter(time_point >= 2) %>%
  ggplot(aes(x = day,
             y = total_regional_bioarea,
             group = day)) +
  geom_boxplot() +
  labs(title = "Without log transformation",
       x = "Day",
       y = "Regional bioarea (something/µl)")

linear_model = lm(total_regional_bioarea ~ 
                    day, 
                  data = ds_regional_biomass %>% 
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"))

par(mfrow=c(2,3))
plot(linear_model, which = 1:5)

Model selection

Let’ start from the full model.

\[ Regional \: bioarea = t + M + D + tM + tD + MD + tDM + (t | system \: nr) \]

full = lmer(total_regional_bioarea ~
                     day * metaecosystem_type * disturbance +
                     (day | system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

Should we keep the correlation in (day | system_nr)?

no_correlation = lmer(total_regional_bioarea ~
                     day * metaecosystem_type * disturbance +
                     (day || system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

anova(full, no_correlation)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_correlation: total_regional_bioarea ~ day * metaecosystem_type * disturbance + ((1 | system_nr) + (0 + day | system_nr))
## full: total_regional_bioarea ~ day * metaecosystem_type * disturbance + (day | system_nr)
##                npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## no_correlation   11 2785.8 2816.5 -1381.9   2763.8                     
## full             12 2786.3 2819.8 -1381.2   2762.3 1.5333  1     0.2156

No.

Should we keep t * M * D?

no_threeway = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     day : metaecosystem_type + 
                     day : disturbance +
                     metaecosystem_type : disturbance + 
                     (day || system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = 'optimx', 
                                         optCtrl = list(method = 'L-BFGS-B')))

anova(no_correlation, no_threeway)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_threeway: total_regional_bioarea ~ day + metaecosystem_type + disturbance + day:metaecosystem_type + day:disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
## no_correlation: total_regional_bioarea ~ day * metaecosystem_type * disturbance + ((1 | system_nr) + (0 + day | system_nr))
##                npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## no_threeway      10 2783.9 2811.8 -1382.0   2763.9                     
## no_correlation   11 2785.8 2816.5 -1381.9   2763.8 0.0906  1     0.7634

No.

Should we keep t * M?

no_TM = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     day : disturbance +
                     metaecosystem_type : disturbance + 
                     (day || system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

anova(no_threeway,no_TM)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_TM: total_regional_bioarea ~ day + metaecosystem_type + disturbance + day:disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
## no_threeway: total_regional_bioarea ~ day + metaecosystem_type + disturbance + day:metaecosystem_type + day:disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
##             npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)   
## no_TM          9 2789.4 2814.5 -1385.7   2771.4                        
## no_threeway   10 2783.9 2811.8 -1382.0   2763.9 7.4715  1   0.006268 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

No.

Should we keep t * D?

no_TD = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     metaecosystem_type : disturbance + 
                     (day || system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))
anova(no_TM, no_TD)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_TD: total_regional_bioarea ~ day + metaecosystem_type + disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
## no_TM: total_regional_bioarea ~ day + metaecosystem_type + disturbance + day:disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
##       npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## no_TD    8 2787.4 2809.7 -1385.7   2771.4                     
## no_TM    9 2789.4 2814.5 -1385.7   2771.4 0.0198  1      0.888

No.

Should we keep M * D?

no_MD = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     (day || system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

anova(no_TD, no_MD)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_MD: total_regional_bioarea ~ day + metaecosystem_type + disturbance + ((1 | system_nr) + (0 + day | system_nr))
## no_TD: total_regional_bioarea ~ day + metaecosystem_type + disturbance + metaecosystem_type:disturbance + ((1 | system_nr) + (0 + day | system_nr))
##       npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## no_MD    7 2785.7 2805.2 -1385.9   2771.7                     
## no_TD    8 2787.4 2809.7 -1385.7   2771.4 0.3286  1     0.5665

No.

Should we keep the random effect of system nr on the time slopes (day | system_nr)?

no_random_slopes = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     (1 | system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

anova(no_MD, no_random_slopes)

## Data: ds_regional_biomass %>% filter(time_point >= 2) %>% filter(metaecosystem_type ==  ...
## Models:
## no_random_slopes: total_regional_bioarea ~ day + metaecosystem_type + disturbance + (1 | system_nr)
## no_MD: total_regional_bioarea ~ day + metaecosystem_type + disturbance + ((1 | system_nr) + (0 + day | system_nr))
##                  npar    AIC    BIC  logLik deviance Chisq Df Pr(>Chisq)
## no_random_slopes    6 2783.7 2800.4 -1385.8   2771.7                    
## no_MD               7 2785.7 2805.2 -1385.9   2771.7     0  1          1

No.

Best model

Therefore, our best model is:

\[ Regional \: bioarea = t + M + D + (t|| system \: nr) \]

The R squared of this model for t2-t7 are:

best_model = no_random_slopes

R2_marginal = r.squaredGLMM(best_model)[1]
R2_marginal = round(R2_marginal, digits = 2)
R2_conditional = r.squaredGLMM(best_model)[2]
R2_conditional = round(R2_conditional, digits = 2)

• Marginal R2 = 0.74

• Conditional R2 = 0.76

Let’s just assume that this model holds also for t2-t5. Then, let’s recalculate the R squared.

t2_t5 = lmer(total_regional_bioarea ~
                     day +
                     metaecosystem_type +
                     disturbance +
                     day : disturbance +
                     (day | system_nr),
                     data = ds_regional_biomass %>%
                            filter(time_point >= 2) %>%
                            filter(time_point <= 5) %>%
                            filter(metaecosystem_type == "M_M" | metaecosystem_type == "S_L"),
                   REML = FALSE,
                   control = lmerControl(optimizer = "Nelder_Mead"))

R2_marginal = r.squaredGLMM(t2_t5)[1]
R2_marginal = round(R2_marginal, digits = 2)
R2_conditional = r.squaredGLMM(t2_t5)[2]
R2_conditional = round(R2_conditional, digits = 2)

The R squared of this model for t2-t5 are:

• Marginal R2 = 0.58

• Conditional R2 = 0.6

Next steps:

• calculating the R2 of the meta-ecosystem type. I was thinking I could do it with part2but it can’t do it when the model has a random slope. -> evaluating whether meta-ecosystem type R2 is high enough -> if it’s not, redo model selection with t2-t5 to see if you can increase R2 of meta-ecosystem type.

Model single points

How does the biomass density of medium-medium and small-large meta-ecosystems differ for each time point? (The first two points before the first disturbance are taken off).

Need to wait until I understand how to calculate R2 for models with random slopes, so then I can look at the R2 of meta-ecosystem type across time points.

full = lmer(log10(total_regional_bioarea + 1) ~
            metaecosystem_type +
            disturbance +
            metaecosystem_type : disturbance +
            (1 | system_nr),
            data = ds_regional_biomass %>%
              filter(time_point == 3) %>%
              filter(metaecosystem_type == "M_M" |
                     metaecosystem_type == "S_L"),
            REML = FALSE)

# Next step: understanding what is a grouping factor. I need to understand what a grouping factor because I cannot run the full model, as it gives me the following problem: "Error: number of levels of each grouping factor must be < number of observations (problems: system_nr)."

Small-Large vs Small-Large from isolated

Do a meta-ecosystem with patches of the same size and a meta-ecosystems with patches of different size have different regional biomass density because of their resource flow? Or would we see this also with small and large ecosystems that are not connected? (Do the small-large meta-ecosystems have different biomass density from two isolated small and large patches?)

Tidy

To create the combinations of small and large isolated patches to be compared to the small-large meta-ecosystems, I’m going through the following steps.

1. Take isolated small and large patches.
2. Because I had to take out the last
3. Add them together randomly (here following numeric order, e.g., small isolated 1 with large isolated 11, small isolated 2 with large isolated 12 and so on). Doing this, we make sure that we are matching their disturbances.

system_nr_to_take_off = 50
n_time_points = 8

isolated_S_and_L = ds_biomass %>%
  filter(!system_nr == system_nr_to_take_off) %>%
  filter(eco_metaeco_type == "S" | eco_metaeco_type == "L") %>%
  group_by(system_nr, disturbance, time_point, day, eco_metaeco_type) %>%
  summarise(bioarea_per_volume_across_videos = mean(bioarea_per_volume))

### --- Low disturbance --- ###

isolated_S_low = isolated_S_and_L %>%
  filter(eco_metaeco_type == "S") %>%
  filter(disturbance == "low")
isolated_L_low = isolated_S_and_L %>%
  filter(eco_metaeco_type == "L") %>%
  filter(disturbance == "low")
  
n_isolated_patches = (nrow(isolated_S_low)) / n_time_points

number_for_pairing_v = rep(1:n_isolated_patches, each = n_time_points)
isolated_S_low$number_for_pairing = number_for_pairing_v  
isolated_L_low$number_for_pairing = number_for_pairing_v 

### --- High disturbance --- ###

isolated_S_high = isolated_S_and_L %>%
  filter(eco_metaeco_type == "S") %>%
  filter(disturbance == "high")
isolated_L_high = isolated_S_and_L %>%
  filter(eco_metaeco_type == "L") %>%
  filter(disturbance == "high")
  
n_isolated_patches = (nrow(isolated_S_high)) / n_time_points
number_for_pairing_v = rep(1:n_isolated_patches, each = n_time_points)
isolated_S_high$number_for_pairing = number_for_pairing_v + 100
isolated_L_high$number_for_pairing = number_for_pairing_v + 100

SL_from_isolated = rbind(isolated_S_low,
                         isolated_L_low,
                         isolated_S_high,
                         isolated_L_high) %>%
  mutate(metaecosystem_type = "S_L_from_isolated") %>%
  rename(total_regional_bioarea = bioarea_per_volume_across_videos)

ds_regional_with_SL_from_isolated = rbind(SL_from_isolated, ds_regional_biomass)

#This would be another way of doing it
system_nr_S_low = unique(isolated_S$system_nr)[1:5]
system_nr_L_low = unique(isolated_L$system_nr)[1:5]
system_nr_S_high = unique(isolated_S$system_nr)[6:9]
system_nr_L_high = unique(isolated_L$system_nr)[6:9]

low_pairs = expand.grid(system_nr_S_low,system_nr_L_low)
high_pairs = expand.grid(system_nr_S_high, system_nr_L_high)
pairs = rbind(low_pairs, high_pairs)
number_of_pairs = nrow(pairs)


SL_from_isolated_all_combinations = NULL
for (pair in 1:number_of_pairs){
  
 SL_from_isolated_one_combination = ds_biomass %>%
  filter(system_nr %in% pairs[pair,]) %>%
  group_by(disturbance, day, time_point, system_nr) %>%
  summarise(regional_bioarea_across_videos = mean(bioarea_per_volume)) %>%
  group_by(disturbance, day, time_point) %>%
  summarise(total_regional_bioarea = mean(regional_bioarea_across_videos)) %>%
  mutate(system_nr = 1000 + pair) %>%
   mutate(metaecosystem_type = "S_L_from_isolated")
 
 SL_from_isolated_all_combinations = rbind(SL_from_isolated_one_combination,
                                          SL_from_isolated_all_combinations)
 
  
}

ds_regional_with_SL_from_isolated = rbind(SL_from_isolated_all_combinations, ds_regional_biomass)

Next step: bootstrap 5 isolated small patches and 5 isolated large patches

Plots

ds_regional_with_SL_from_isolated %>%
    filter ( disturbance == "low") %>%
    filter (metaecosystem_type == "S_L" | metaecosystem_type == "S_L_from_isolated") %>%
    ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
                color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (µm²?)",
         title = "Disturbance = low",
         fill = "System nr",
         color = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
    scale_linetype_discrete(labels = c("small-large",
                                     "small-large \n from isolated")) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

ds_regional_with_SL_from_isolated %>%
    filter ( disturbance == "high") %>%
    filter (metaecosystem_type == "S_L" | metaecosystem_type == "S_L_from_isolated") %>%
    ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
                color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(title = "Disturbance = high",
         x = "Day", 
         y = "Regional bioarea (µm²?)",
         fill = "System nr",
         color = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
    scale_linetype_discrete(labels = c("small-large",
                                     "small-large \n from isolated")) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

ds_regional_with_SL_from_isolated %>%
  filter(disturbance == "low") %>%
  filter(metaecosystem_type == "S_L" | metaecosystem_type == "S_L_from_isolated") %>%
  ggplot(aes(x = day,
             y = total_regional_bioarea,
             group = interaction(day, metaecosystem_type),
             fill = metaecosystem_type)) +
  geom_boxplot() +
  labs(title = "Disturbance = low",
       x = "Day",
       y = "Regional bioarea (µm²?)",
       fill = "") +
  scale_fill_discrete(labels = c("small-large", "isolated small & \n isolated large")) + 
  theme_bw() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(),
        legend.position = c(.95, .95),
        legend.justification = c("right", "top"),
        legend.box.just = "right",
        legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

ds_regional_with_SL_from_isolated %>%
  filter(disturbance == "high") %>%
  filter(metaecosystem_type == "S_L" | metaecosystem_type == "S_L_from_isolated") %>%
  ggplot(aes(x = day,
             y = total_regional_bioarea,
             group = interaction(day, metaecosystem_type),
             fill = metaecosystem_type)) +
  geom_boxplot() +
  labs(title = "Disturbance = high",
       x = "Day",
       y = "Regional bioarea (µm²?)",
       fill = "") +
  scale_fill_discrete(labels = c("small-large", "isolated small & \n isolated large")) + 
  theme_bw() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(),
        legend.position = c(.95, .95),
        legend.justification = c("right", "top"),
        legend.box.just = "right",
        legend.margin = margin(6, 6, 6, 6)) +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

The plots broke when I tried to do the bootstrapping.

Modelling

The model broke when I tried to do the bootstrapping.

mixed_model = lmer(log10(total_regional_bioarea +1) ~ 
                     day * metaecosystem_type * disturbance +
                     (day | system_nr),
                   data = ds_regional_with_SL_from_isolated %>%
                     filter(metaecosystem_type == "S_L" | 
                              metaecosystem_type == "S_L_from_isolated") %>%
                     filter(time_point >= 2),
                   REML = FALSE,
                   control = lmerControl (optimizer = "Nelder_Mead"))

null_model = lmer(log10(total_regional_bioarea +1) ~ 
                     day * disturbance +
                     (day | system_nr),
                   data = ds_regional_with_SL_from_isolated %>%
                     filter(metaecosystem_type == "S_L" | 
                              metaecosystem_type == "S_L_from_isolated") %>%
                     filter(time_point >= 2),
                   REML = FALSE,
                   control = lmerControl (optimizer = "Nelder_Mead"))
anova(mixed_model, null_model)

Meta-ecosystems of different total size

How does the biomass density of meta-ecosystems change according to the size of their patches?

ds_regional_biomass %>%
  filter(!metaecosystem_type == "S_L") %>%
  filter ( disturbance == "low") %>%
  ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
              color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (µm²?)",
         title = "Disturbance = low",
         fill = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
  scale_colour_continuous(guide = "none") +
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_linetype_discrete(labels = c("large-large",
                                     "medium-medium",
                                     "small-small"))  +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

## Warning: Removed 110 row(s) containing missing values (geom_path).

ds_regional_biomass %>%
  filter(!metaecosystem_type == "S_L") %>%
  filter ( disturbance == "high") %>%
  ggplot (aes(x = day,
                y = total_regional_bioarea,
                group = system_nr,
                fill = system_nr,
              color = system_nr,
                linetype = metaecosystem_type)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (µm²?)",
         title = "Disturbance = high",
         fill = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
    scale_colour_continuous(guide = "none") +
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_linetype_discrete(labels = c("large-large",
                                     "medium-medium",
                                     "small-small"))  +
  geom_vline(xintercept = first_perturbation_day, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

## Warning: Removed 104 row(s) containing missing values (geom_path).

ds_regional_biomass %>%
  filter(disturbance == "low") %>%
  filter(!metaecosystem_type == "S_L") %>%
  ggplot(aes(x = day,
             y = total_regional_bioarea,
             group = interaction(day, metaecosystem_type),
             fill = metaecosystem_type)) +
  geom_boxplot() + 
  labs(title = "Disturbance = low",
       x = "Day",
       y = "Regional bioarea (µm²?)",
       fill = "") + 
  #scale_fill_discrete(labels = c("isolated large", "isolated medium", "isolated small")) +
  theme_bw() + 
  theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_fill_discrete(labels = c("large-large",
                                 "medium-medium",
                                 "small-small")) +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

ds_regional_biomass %>%
  filter(disturbance == "high") %>%
  filter(!metaecosystem_type == "S_L") %>%
  ggplot(aes(x = day,
             y = total_regional_bioarea,
             group = interaction(day, metaecosystem_type),
             fill = metaecosystem_type)) +
  geom_boxplot() + 
  labs(title = "Disturbance = high",
       x = "Day",
       y = "Regional bioarea (µm²?)",
       fill = "") + 
  #scale_fill_discrete(labels = c("isolated large", "isolated medium", "isolated small")) +
  theme_bw() + 
  theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_fill_discrete(labels = c("large-large",
                                 "medium-medium",
                                 "small-small")) +
  geom_vline(xintercept = first_perturbation_day + 0.7, 
             linetype="dotdash", 
             color = "grey", 
             size=0.7) +
  labs(caption = "Vertical grey line: first perturbation")

Interesting. It seems like there’s not much difference between the medium-medium and the large-large.

Local biomass

Small patches

How does biomass density change according to the size to which the patch is connected? (Does a small patch connected to a small patch have the same biomass density than a small patch connected to a large patch?)

Large patches

How does biomass density change according to the size to which the patch is connected? (Does a large patch connected to a large patch have the same biomass density than a large patch connected to a small patch?)

Isolated patches

How does biomass density change according to the size of isolated patches? (How does the biomass of small, medium, and large patches change?)

ds_biomass %>%
  filter ( disturbance == "low") %>%
  filter(metaecosystem == "no") %>%
  group_by (system_nr, day, patch_size) %>%
  summarise(mean_bioarea_per_volume_across_videos = mean(bioarea_per_volume)) %>%
  ggplot (aes(x = day,
                y = mean_bioarea_per_volume_across_videos,
                group = system_nr,
                fill = system_nr,
              color = system_nr,
                linetype = patch_size)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (something/µl)",
         title = "Disturbance = low",
         fill = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
  scale_colour_continuous(guide = "none") +
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_linetype_discrete(labels = c("large isolated",
                                     "medium isolated",
                                     "small isolated"))

ds_biomass %>%
  filter ( disturbance == "high") %>%
  filter(metaecosystem == "no") %>%
  group_by (system_nr, day, patch_size) %>%
  summarise(mean_bioarea_per_volume_across_videos = mean(bioarea_per_volume)) %>%
  ggplot (aes(x = day,
                y = mean_bioarea_per_volume_across_videos,
                group = system_nr,
                fill = system_nr,
              color = system_nr,
                linetype = patch_size)) +
    geom_line () +
    labs(x = "Day", 
         y = "Regional bioarea (something/µl)",
         title = "Disturbance = low",
         fill = "System nr",
         linetype = "") +
    scale_y_continuous(limits = c(0, 6250)) +
    scale_x_continuous(limits = c(-2, 30)) +
  scale_colour_continuous(guide = "none") +
    theme_bw() +
    theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  scale_linetype_discrete(labels = c("large isolated",
                                     "medium isolated",
                                     "small isolated"))

ds_biomass %>%
  filter(disturbance == "low") %>%
  filter(metaecosystem == "no") %>%
  ggplot(aes(x = day,
             y = bioarea_per_volume,
             group = interaction(day, patch_size),
             fill = patch_size)) +
  geom_boxplot() + 
  labs(title = "Disturbance = low",
       x = "Day",
       y = "Local bioarea (something/μl)",
       fill = "") + 
  scale_fill_discrete(labels = c("isolated large", "isolated medium", "isolated small")) +
  theme_bw() + 
  theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6))

ds_biomass %>%
  filter(disturbance == "high") %>%
  filter(metaecosystem == "no") %>%
  ggplot(aes(x = day,
             y = bioarea_per_volume,
             group = interaction(day, patch_size),
             fill = patch_size)) +
  geom_boxplot() + 
  labs(title = "Disturbance = high",
       x = "Day",
       y = "Local bioarea (something/μl)",
       fill = "") + 
  scale_fill_discrete(labels = c("isolated large", "isolated medium", "isolated small")) +
  theme_bw() + 
  theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6))

Evaporation

Was the amount of evaporation different across different treatments and time points?

We want to know if there was a systematic bias in the evaporation of different treatments (disturbance, patch size) and whether evaporation changed across time. My expectation would be that we would see a difference among the exchanges 2,3 and the exchanges 4,5,6. This is because in exchange 2,3 cultures were microwaved in 15 tubes for 3 minutes and in exchange 4,5,6 cultures were microwaved in 4 tubes for only 1 minute.

Tidy

#Columns: exchange & evaporation
ds_for_evaporation = gather(ds_for_evaporation, 
                            key = exchange, 
                            value = evaporation, 
                            water_add_after_t2:water_add_after_t6)
ds_for_evaporation[ds_for_evaporation == "water_add_after_t2"] = "2"
ds_for_evaporation[ds_for_evaporation == "water_add_after_t3"] = "3"
ds_for_evaporation[ds_for_evaporation == "water_add_after_t4"] = "4"
ds_for_evaporation[ds_for_evaporation == "water_add_after_t5"] = "5"
ds_for_evaporation[ds_for_evaporation == "water_add_after_t6"] = "6"
ds_for_evaporation$evaporation[ds_for_evaporation$exchange == 2] = ds_for_evaporation$evaporation[ds_for_evaporation$exchange == 2] / 2 #This is because exchange contained the topping up of two exchanges
ds_for_evaporation$evaporation[ds_for_evaporation$exchange == 2] = ds_for_evaporation$evaporation[ds_for_evaporation$exchange == 2] + 2 #We need to add 2 ml to the evaporation that happened at the exchange events 1 and 2. This is because we already added 1 ml of water at exchange 1 and 1 ml of water at exchange 2. 

#Column: nr_of_tubes_in_rack
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 1] = 15
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 2] = 15
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 3] = 15
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 4] = 4
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 5] = 4
ds_for_evaporation$nr_of_tubes_in_rack[ds_for_evaporation$exchange == 6] = 4

Plot

ds_for_evaporation %>%
  filter(disturbance == disturbance) %>%
  ggplot(aes(x = as.character(nr_of_tubes_in_rack),
             y = evaporation)) + 
  geom_boxplot() + 
  labs(x = "Number of tubes in rack", 
       y = "Evaporation (ml)")

ds_for_evaporation %>%
  filter(disturbance == disturbance) %>%
  ggplot(aes(x = as.character(patch_size),
             y = evaporation)) + 
  geom_boxplot() + 
  labs(x = "Patch size", 
       y = "Evaporation (ml)")

ds_for_evaporation %>%
  filter(disturbance == disturbance) %>%
  ggplot(aes(x = as.character(day),
             y = evaporation)) + 
  geom_boxplot() + 
  labs(x = "Day", 
       y = "Evaporation (ml)")

ds_for_evaporation %>%
  filter(disturbance == disturbance) %>%
  ggplot(aes(x = disturbance,
             y = evaporation)) + 
  geom_boxplot() + 
  labs(x = "Disturbance", 
       y = "Evaporation (ml)")

It seems like there is no real difference across time, disturbance, or patch type. However, we could also run a mixed effect model to show that they do not.

Mixed effect model

It gives me the following error:

• Error in fn(nM$xeval()) : Downdated VtV is not positive definite

mixed.model = lmer(evaporation  ~ 
                     patch_size * disturbance  * exchange + 
                     (exchange | culture_ID), 
                   data = ds_for_evaporation,
                   REML = FALSE, 
                   control = lmerControl (optimizer = "Nelder_Mead"))

null.model = lm(evaporation ~
                  1, 
                data = ds_for_evaporation)

anova(mixed.model, null.model)

Body size

Aim

Data

Experimental cultures

culture_info = read.csv(here("data", "PatchSizePilot_culture_info.csv"), header = TRUE)
load(here("data", "morphology", "t0.RData"));t0 = morph_mvt
load(here("data", "morphology", "t1.RData"));t1 = morph_mvt
load(here("data", "morphology", "t2.RData"));t2 = morph_mvt
load(here("data", "morphology", "t3.RData"));t3 = morph_mvt
load(here("data", "morphology", "t4.RData"));t4 = morph_mvt
load(here("data", "morphology", "t5.RData"));t5 = morph_mvt
load(here("data", "morphology", "t6.RData"));t6 = morph_mvt
load(here("data", "morphology", "t7.RData"));t7 = morph_mvt
rm(morph_mvt)

datatable(culture_info[,1:10],
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Body size data-set

### --- Tidy t0 - t7 data-sets --- ###

#Column: time
t0$time = NA
t1$time = NA

#Column: replicate_video
t0$replicate_video[t0$file == "sample_00001"] = 1
t0$replicate_video[t0$file == "sample_00002"] = 2
t0$replicate_video[t0$file == "sample_00003"] = 3
t0$replicate_video[t0$file == "sample_00004"] = 4
t0$replicate_video[t0$file == "sample_00005"] = 5
t0$replicate_video[t0$file == "sample_00006"] = 6
t0$replicate_video[t0$file == "sample_00007"] = 7
t0$replicate_video[t0$file == "sample_00008"] = 8
t0$replicate_video[t0$file == "sample_00009"] = 9
t0$replicate_video[t0$file == "sample_00010"] = 10
t0$replicate_video[t0$file == "sample_00011"] = 11
t0$replicate_video[t0$file == "sample_00012"] = 12
t1$replicate_video = 1 #In t1 I took only 1 video/culture
t2$replicate_video = 1 #In t2 I took only 1 video/culture
t3$replicate_video = 1 #In t3 I took only 1 video/culture
t4$replicate_video = 1 #In t4 I took only 1 video/culture
t5$replicate_video = 1 #In t5 I took only 1 video/culture
t6 = t6 %>% rename(replicate_video = replicate)
t7 = t7 %>% rename(replicate_video = replicate)


### --- Create ds_body_size dataset --- ###

long_t0 = t0 %>% slice(rep(1:n(), max(culture_info$culture_ID)))
ID_vector = NULL
ID_vector_elongating = NULL
for (ID in 1:max(culture_info$culture_ID)){
  ID_vector = rep(ID, times = nrow(t0))
  ID_vector_elongating = c(ID_vector_elongating, ID_vector)
}
long_t0$culture_ID = ID_vector_elongating
t0 = merge(culture_info,long_t0, by="culture_ID"); rm(long_t0)
t1 = merge(culture_info,t1,by="culture_ID")
t2 = merge(culture_info,t2,by="culture_ID")
t3 = merge(culture_info,t3,by="culture_ID")
t4 = merge(culture_info,t4,by="culture_ID")
t5 = merge(culture_info,t5,by="culture_ID")
t6 = merge(culture_info,t6,by="culture_ID")
t7 = merge(culture_info,t7,by="culture_ID")
ds_body_size = rbind(t0, t1, t2, t3, t4, t5, t6, t7); rm(t0, t1, t2, t3, t4, t5, t6, t7)

### --- Tidy ds_body_size data-set --- ###

#Column: day
ds_body_size$day = ds_body_size$time_point;
ds_body_size$day[ds_body_size$day=="t0"] = "0"
ds_body_size$day[ds_body_size$day=="t1"] = "4"
ds_body_size$day[ds_body_size$day=="t2"] = "8"
ds_body_size$day[ds_body_size$day=="t3"] = "12"
ds_body_size$day[ds_body_size$day=="t4"] = "16"
ds_body_size$day[ds_body_size$day=="t5"] = "20"
ds_body_size$day[ds_body_size$day=="t6"] = "24"
ds_body_size$day[ds_body_size$day=="t7"] = "28"
ds_body_size$day = as.numeric(ds_body_size$day)

#Column: time point
ds_body_size$time_point[ds_body_size$time_point=="t0"] = 0
ds_body_size$time_point[ds_body_size$time_point=="t1"] = 1
ds_body_size$time_point[ds_body_size$time_point=="t2"] = 2
ds_body_size$time_point[ds_body_size$time_point=="t3"] = 3
ds_body_size$time_point[ds_body_size$time_point=="t4"] = 4
ds_body_size$time_point[ds_body_size$time_point=="t5"] = 5
ds_body_size$time_point[ds_body_size$time_point=="t6"] = 6
ds_body_size$time_point[ds_body_size$time_point=="t7"] = 7
ds_body_size$time_point = as.character(ds_body_size$time_point)

#Column: eco_metaeco_type
ds_body_size$eco_metaeco_type = factor(ds_body_size$eco_metaeco_type, 
                             levels=c('S', 'S (S_S)', 'S (S_L)', 'M', 'M (M_M)', 'L', 'L (L_L)', 'L (S_L)'))

#Select useful columns
ds_body_size = ds_body_size %>% 
  select(culture_ID, 
         patch_size, 
         disturbance, 
         metaecosystem_type, 
         mean_area, 
         replicate_video, 
         day, 
         metaecosystem, 
         system_nr, 
         eco_metaeco_type)

#Reorder columns
ds_body_size = ds_body_size[, c("culture_ID", 
            "system_nr", 
            "disturbance", 
            "day",
            "patch_size", 
            "metaecosystem", 
            "metaecosystem_type", 
            "eco_metaeco_type", 
            "replicate_video",
            "mean_area")]

datatable(ds_body_size,
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

## Warning in instance$preRenderHook(instance): It seems your data is too big
## for client-side DataTables. You may consider server-side processing: https://
## rstudio.github.io/DT/server.html

Size classes data-set

I am here creating 12 size classes as in Jacquet, Gounand, and Altermatt (2020). However, for some reason it seems like our body size classes are really different.

#### --- PARAMETERS & INITIALISATION --- ###

nr_of_size_classes = 12
largest_size = max(ds_body_size$mean_area)
size_class_width = largest_size/nr_of_size_classes
size_class = NULL

### --- CREATE DATASET --- ###

size_class_boundaries = seq(0, largest_size, by = size_class_width)

for (class in 1:nr_of_size_classes){
  
  bin_lower_limit = size_class_boundaries[class]
  bin_upper_limit = size_class_boundaries[class+1]
  size_input = (size_class_boundaries[class] + size_class_boundaries[class + 1])/2
  
  size_class[[class]] = ds_body_size%>%
    filter(bin_lower_limit <= mean_area) %>%
    filter(mean_area <= bin_upper_limit) %>%
    group_by(culture_ID, 
             system_nr, 
             disturbance, 
             day, 
             patch_size, 
             metaecosystem, 
             metaecosystem_type, 
             eco_metaeco_type, 
             replicate_video) %>% #Group by video
    summarise(mean_abundance_across_videos = n()) %>%
    group_by(culture_ID, 
             system_nr, 
             disturbance, 
             day, 
             patch_size, 
             metaecosystem, 
             metaecosystem_type, 
             eco_metaeco_type) %>% #Group by ID
    summarise(abundance = mean(mean_abundance_across_videos)) %>%
    mutate(log_abundance = log(abundance)) %>%
    mutate(size_class = class) %>%
    mutate(size = size_input) %>%
    mutate(log_size = log(size))
  
}

ds_classes = rbind(size_class[[1]], size_class[[2]], size_class[[3]], size_class[[4]],
                  size_class[[5]], size_class[[6]], size_class[[7]], size_class[[8]],
                  size_class[[9]], size_class[[10]], size_class[[11]], size_class[[12]],)

datatable(ds_classes,
          rownames = FALSE,
          options = list(scrollX = TRUE),
          filter = list(position = 'top', 
                        clear = FALSE))

Plot

Comparison of different ecosystem types across time

#Trying out gganimate, but I can't seem to manage to install transformr packaget
p = list()
n = 0
first_level = c("isolated small", "isolated small", "isolated large", "isolated large")
second_level = c("small connected to small", "small connected to small", "large connected to large", "large connected to large")
third_level = c("small connected to large", "small connected to large", "large connected to small", "large connected to small")
for (patch_size_input in c("S", "L")){
  
  for(disturbance_input in c("low", "high")){
  
    n = n + 1
      
  title = paste0(patch_size_input,
              ' patches, Disturbance = ',
              disturbance_input, 
              ', Day: {round(frame_time, digits = 0)}')
  
  p[[n]] <- ds_classes %>%
  filter(disturbance == disturbance_input) %>%
  filter(patch_size == patch_size_input) %>%
  ggplot(aes(x = log_size,
             y = log_abundance,
             group = interaction(log_size, eco_metaeco_type),
             color = eco_metaeco_type)) +
  geom_point(stat = "summary", fun = "mean") +
  geom_line(stat = "summary", fun = "mean", aes(group=eco_metaeco_type)) +
  scale_color_discrete(labels = c(first_level[n], 
                                 second_level[n],
                                 third_level[n])) +
  theme_bw() +
  theme(panel.grid.major = element_blank(), 
          panel.grid.minor = element_blank(),
          legend.position = c(.95, .95),
          legend.justification = c("right", "top"),
          legend.box.just = "right",
          legend.margin = margin(6, 6, 6, 6)) +
  labs(title = title,
       x = 'Log size (μm2)', 
       y = 'Log abundance + 1 (indiv/μm2)',
       color = "") +
  transition_time(day) +
  ease_aes('linear')
  
  animate(p[[n]], 
        duration = 10,
        fps = 25, 
        width = 500, 
        height = 500, 
        renderer = gifski_renderer())
  
  anim_save(here("gifs", 
                 paste0("transition_day_", 
                        patch_size_input,"_", 
                        disturbance_input, 
                        ".gif")))
}
}

• Next step: making plots slower (the package stopped working because I broke some dependencies)

Figures

Regional biomass under low disturbance in meta-ecosystems of the same total area, but exhibiting two local patches of the same size (red, medium-medium meta-ecosystem) or different size (blue, small-large meta-ecosystem). Points represent the mean, error bars represent the standard deviation. See the Appendix for equivalent figure of the high disturbance treatment.

Tests

Evaporation when microwaving 15 falcon tubes at the time

evaporation.test = read.csv(here("data", "evaporation_test","evaporation_test_right.csv"), header = TRUE)

evaporation.test %>%
  ggplot(aes (x = as.character(water_pipetted),
                y = weight_water_evaporated,
                group = interaction(water_pipetted, as.character(rack)),
                fill = as.character(rack))) +
  geom_boxplot() +
  labs(x = "Water volume (ml)" , 
       y = "Evaporation (g)", 
       fill = "Rack replicate")

Evaporation when microwaving 5 tubes with 10 filled or empty tubes

evaporation.test = read.csv(here("data", "evaporation_test", "evaporation_test_fill_nofill.csv"), header = TRUE)

evaporation.test %>%
  ggplot(aes (x = all_tubes_water,
              y = weight_water_evaporated)) +
  geom_boxplot() +
  labs(x = "Water in the other 10 tubes" , 
  y = "Evaporation (g)", 
  caption = "When all tubes were filled, they were filled with 6.75 ml of deionised water.")

Running time

## Time difference of 25.52575 secs

Other

Mixed effects models

• To build the mixed effect models we will use the R package lme4. See page 6 of this PDF to know more about the syntaxis of this package and this link for the interaction syntaxis.

• To do model diagnostics of mixed effect models, I’m going to look at the following two plots (as suggested by Zuur et al. (2009), page 487):

  • Quantile-quantile plots (plot(mixed_model))

  • Partial residual plots (qqnorm(resid(mixed_model)))

• The effect size of the explaining variables is calculated in the mixed effect models as marginal and conditional r squared. The marginal r squared is how much variance is explained by the fixed effects. The conditional r squared is how much variance is explained by the fixed and the random effects. The marginal and conditional r squared are calculated using the package MuMIn. The computation is based on the methods of Nakagawa, Johnson, and Schielzeth (2017). For the coding and interpretation of these r squared check the documentation for the r.squaredGLMM function

• Time can be included as a fixed or random effect. Time can be included as a random effect if the different data points are non independent from each other (e.g., seasons). However, because the biomass in our experiment was following a temporal trend, the different time points show autocorrelation. In other words, t2 is more similar to t3 than t4 and so on. This is why we decided to include time as a fixed effect. For an excellent discussion on this topic see this blog post.

Modeling choices

• I am going to select the best model according to AIC. Halsey (2019) suggests this approach instead of p values. P-values are not a reliable way of choosing a model because:

  • My sample size is small, producing larger p-values

  • P-values are really variable, creating many false positives and negatives (e.g., if p=0.05 there is a 1 in 3 chance that it’s a false positive)

• To study the local biomass how it changes across treatments, we could have made three different models between the three combinations of small patches. However, that might be confusing to interpret the results. We decided instead to use an effect size where we control is the isolated small patch. At the beginning we thought to use the natural logarithm of the response ratio (lnRR). The problem, however, is that some bioarea values were 0. We were thinking to add 1 to all null values, but according to Rosenberg, Rothstein, and Gurevitch (2013), such practice inflates effect sizes. Because of this, I looked into other types of effect size. I found that the most common and preferred metric in use today is known as Hedge’s d (a.k.a. Hedge’s g) (Hedges, Larry V. and Olkin (1985) ). It is calculated as the difference in mean between treatment and control divided by the standard deviation of the pooled data. Another measure would be Cohen’s d, but it underperforms with sample sizes that are lower than 20 (StatisticsHowTo). I can easily calculate the Hedge’s d using the r package effsize.
  Same thing for the large patches.

Bibliography

Halsey, Lewis G. 2019. “The reign of the p-value is over: What alternative analyses could we employ to fill the power vacuum?” Biology Letters 15 (5). https://doi.org/10.1098/rsbl.2019.0174.

Hedges, Larry V., and Ingram Olkin. 1985. Statistical Methods for Meta-Analysis.

Jacquet, Claire, Isabelle Gounand, and Florian Altermatt. 2020. “How pulse disturbances shape size-abundance pyramids.” Ecology Letters 23 (6): 1014–23. https://doi.org/10.1111/ele.13508.

Nakagawa, Shinichi, Paul C. D. Johnson, and Holger Schielzeth. 2017. “The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.” Journal of the Royal Society Interface 14 (134). https://doi.org/10.1098/rsif.2017.0213.

Rosenberg, Michael S., Hannah R. Rothstein, and Jessica Gurevitch. 2013. “Effect sizes: Conventional choices and calculations.” Handbook of Meta-Analysis in Ecology and Evolution, 61–71. https://doi.org/10.23943/princeton/9780691137285.003.0006.

Zuur, Alain F., Elena N. Ieno, Neil Walker, Anatoly A. Saveliev, and Graham M. Smith. 2009. Mixed effects models and extensions in ecology with R. Vol. 36. Statistics for Biology and Health. New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-87458-6.